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(x(x*arctgx-1)+arctgx)/2
Derivada de la función/ arctg/ ctgx-1/ (x(x*arctgx-1)+arctgx)/2

Derivada de (x(x*arctgx-1)+arctgx)/2

Función f() - derivada -er orden en el punto
v

Gráfico:

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Solución

Ha introducido [src] 
x*(x*acot(x) - 1) + acot(x)
---------------------------
             2
x(xacot⁡(x)−1)+acot⁡(x)2\frac{x \left(x \operatorname{acot}{\left(x \right)} - 1\right) + \operatorname{acot}{\left(x \right)}}{2} 
(x*(x*acot(x) - 1) + acot(x))/2
Gráfica
02468-8-6-4-2-10102-2
Trazar el gráfico f(x)
Trazar el gráfico f'(x)
Primera derivada [src] 
                     /    x             \            
                   x*|- ------ + acot(x)|            
                     |       2          |            
  1       1          \  1 + x           /   x*acot(x)
- - - ---------- + ---------------------- + ---------
  2     /     2\             2                  2    
      2*\1 + x /
x(−xx2+1+acot⁡(x))2+xacot⁡(x)2−12−12(x2+1)\frac{x \left(- \frac{x}{x^{2} + 1} + \operatorname{acot}{\left(x \right)}\right)}{2} + \frac{x \operatorname{acot}{\left(x \right)}}{2} - \frac{1}{2} - \frac{1}{2 \left(x^{2} + 1\right)}
Simplificar
Segunda derivada [src] 
                       /        2  \          
                       |       x   |          
                     x*|-1 + ------|          
                       |          2|          
    x         x        \     1 + x /          
--------- - ------ + --------------- + acot(x)
        2        2             2              
/     2\    1 + x         1 + x               
\1 + x /
x(x2x2+1−1)x2+1−xx2+1+x(x2+1)2+acot⁡(x)\frac{x \left(\frac{x^{2}}{x^{2} + 1} - 1\right)}{x^{2} + 1} - \frac{x}{x^{2} + 1} + \frac{x}{\left(x^{2} + 1\right)^{2}} + \operatorname{acot}{\left(x \right)}
Simplificar
Tercera derivada [src] 
 /                                       /        2  \\ 
 |                                     2 |       x   || 
 |                                  4*x *|-1 + ------|| 
 |                 2          2          |          2|| 
 |      1       3*x        4*x           \     1 + x /| 
-|3 - ------ - ------ + --------- + ------------------| 
 |         2        2           2              2      | 
 |    1 + x    1 + x    /     2\          1 + x       | 
 \                      \1 + x /                      / 
--------------------------------------------------------
                              2                         
                         1 + x
−4x2(x2x2+1−1)x2+1−3x2x2+1+4x2(x2+1)2+3−1x2+1x2+1- \frac{\frac{4 x^{2} \left(\frac{x^{2}}{x^{2} + 1} - 1\right)}{x^{2} + 1} - \frac{3 x^{2}}{x^{2} + 1} + \frac{4 x^{2}}{\left(x^{2} + 1\right)^{2}} + 3 - \frac{1}{x^{2} + 1}}{x^{2} + 1}
Simplificar
Gráfico
Derivada de (x(x*arctgx-1)+arctgx)/2
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